Prof. Chunming Zhang:On simultaneous calibration of two-sample t-tests for high-dimension low-sample

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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Chunming Zhang，University of Wisconsin-Madison, USA
Inviter:	陈敏研究员
Title:	On simultaneous calibration of two-sample t-tests for high-dimension low-sample-size data
Time & Venue:	2020.01.06 16:00 N620
Abstract:	Two-sample t-tests have been widely used in research practice and applications. This paper addresses new issues in simultaneously calibrating a diverging number m of two-sample t-statistics for simultaneous inference of significance in high-dimension low-sample size data. For the Gaussian calibration method, we demonstrate that (a) the simultaneous "general" two-sample t-statistics achieve the overall significance level, if log(m) increases at a strictly slower rate than (n_1+n_2)^{1/3} as n_1+n_2 diverges; (b) however, directly applying the same calibration method to simultaneous "pooled" two-sample t-statistics may substantially lose the overall level accuracy. The proposed "adaptively pooled" two-sample t-statistics overcome such incoherence, whereas operate as simply as but perform as well as the "general" two-sample t-statistics. (c) Moreover, we propose a "two-stage" t-test procedure to effectively alleviate the skewness effects commonly encountered from various two-sample t-statistics in practice, thus enhancing the calibration accuracy. Implications of these results are illustrated using both simulation studies and real-data applications.